Fixed-time output synchronization of multilayered coupled networks with quaternion: An exponential quantized scheme

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In this article, the output synchronization of multi-layer coupled quaternion-valued neural networks with or without target state is discussed in fixed or prescribed time by developing a nonseparation approach and applying quantitative control. Firstly, considering the inaccessibility of network states and the diversity of individual functions, a type of quaternion-valued coupled networks with output coupling and multi-layer structure is introduced. In terms of fixed-time or preassigned-time controller design, an exponential quantization protocol without linear feedback is directly designed in the field of quaternion for the addressed networks with the presence of synchronous target, and a distributed quaternion-valued exponential control scheme with finite control gains is developed for the multilayered networks with the absence of synchronous target. In the process of convergence analysis, without utilizing the traditional separation method, some different forms of Lyapunov functions are directly constructed and the technique of Taylor expansion is used to derive the output synchronization criteria and the estimate of convergence time. One specific example is shown at last to verify the developed results.